Question Stem for Question Nos. 9 and 10
Question Stem
Consider the lines \( L_{1} \) and \( L_{2} \) defined by
\[
L_{1}: x \sqrt{2}+y-1=0 \text { and } L_{2}: x \sqrt{2}-y+1=0
\]
For a fixed constant \( \lambda \), let \( C \) be the locus of a point \( P \) such that the product of the distance of \( P \) from \( L_{1} \) and the distance of \( P \) from \( L_{2} \) isin \( \lambda^{2} \). The line \( y=2 x+1 \) meets \( C \) at two points \( R \) and \( S \), where the distance between \( R \) and \( S \) is \( \sqrt{270} \)
Let the perpendicular bisector of \( R S \) meet \( C \) at two distinct points \( R^{\prime} \) and \( S^{\prime} \). Let \( D \) be the square of the distance between \( R^{\prime} \) and \( S^{\prime} \).
Q. 9 The value of \( \lambda^{2} \) is
Q. 10 The value of \( D \) is
